Question

A tourist is walking at a speed of 1.3 m/s along a 9.0-km path that follows an old canal. If the speed of light in a vacuum were 3.0 m/s, how long would the path be, according to the tourist?

Answer 1

Answer:

The length of path according to the tourist is 8111.10 meters.

Explanation:

It is given that,

Speed of tourist, v = 1.3 m/s

Path length, L₀ = 9 km = 9000 m

If the speed of light in a vacuum were 3.0 m/s. We need to find the length of path according to the tourist. Let it is L. It is a case of length contraction.

So, $L=L_0\sqrt{1-\dfrac{v^2}{c^2}}$

$L=9000\times \sqrt{1-\dfrac{(1.3)^2}{(3)^2}}$

L = 8111.10 m

So, the length of path according to the tourist is 8111.10 meters. Hence, this is the required solution.

Answer 2

Answer:

The length is 8111.1 m.

Explanation:

Given that,

Speed of tourist = 1.3 m/s

Distance = 9.0 km

Speed of light = 3.0 m/s

We need to calculate the length

Using formula of length

$L= L_{0}\sqrt{1-(\dfrac{v}{c})^2}$

Where, l = length

$L_{0}$=original length

v = speed of tourist

c = speed of light

Put the value into the formula

$L=9000\times\sqrt{1-(\dfrac{1.3}{3.0})^2}$

$L=8111.1\ m$

Hence, The length is 8111.1 m.